How to keep the object size constant while it is moving?
If you  place your pivot point at the camera ( e.g. 3D cursor to camera, then '3D Cursor' selected as pivot center), when you scale your object in all axes (or any element of it, in edit mode,) the shape will not appear to change in perspective, when seen through the camera. If you then want to 'scale the object manually', you can do that in some other space, say, by setting the pivot to 'Median Point'.